In unmanned aerial vehicle (UAV) navigation, achieving high positioning accuracy is crucial but can be hindered by dynamic environmental uncertainties. This paper introduces DeepCovPG, a novel framework that leverages deep learning and Ultra-Wideband (UWB) technology to enhance positioning precision significantly. At its core, DeepCovPG incorporates a novel neural network architecture, combining Variational Autoencoder (VAE) with Long Short-Term Memory (LSTM) network, to refine UWB range data by noise reduction and dynamic covariance prediction. This approach integrates a dynamic covariance model within the pose graph optimization process, diverges from conventional static uncertainty approaches, enhancing adaptability to environmental shifts and measurement errors. Tested across various settings, including indoor spaces and urban landscapes, DeepCovPG demonstrated a significant 51% reduction in Root Mean Square Error (RMSE) and substantial Mean Absolute Error (MAE) improvements over traditional methods, proving its effectiveness in tackling signal interference and navigational challenges for reliable UAV positioning.